This One To Itself And That One To Itself

Consider all pairs \((a, b)\) of natural numbers such that the product \({ a }^{ a }{ b }^{ b }\), written in base 10, ends in exactly 98 zeroes. If there is only one pair \((a, b)\) for which the product \(ab\) is smallest, then find \(a + b\).

Note: \((4, 5)\) and \((5, 4)\) are considered as one pair. Order does not matter.

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